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HAND BOOK 



NDUSTRIAL DRAWING 



IJJA .1. TBW 







LIBRARY OF CONGRESS. 

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UNITED STATES OF AMERICA. 



HAND- BOOK 



NDUSTRIAL DRAWING 



FOR TEACHERS IN COMMON SCHOOLS. 




/ J^tyi^O'lZ. 



By IDA A. TEW, 
II 

SUPERVISOR OF DRAWING IN PUBLIC SCHOOLS, BEATRICE, NEBRASKA. 



BEATRICE, NEB.: 

EXPRESS PUBLISHING COMPANY, 

1894. 



Copyright, 1894, by 
Ida a. Tew. 






V,Ji 



Contents. 



Introduction, - . . . _ ^ 

Geometric Definitions, - - - - ii 
Construction of Simple, Plane Figures without the 

Use of Compasses, - - - - 22 
Plane Figures to be Constructed Accurately with 

Instruments, - - - - - 26 

Working Drawings, .... ^o 

Development, - ~ - - - "39 

Botanical Drawing, - - - . . ^y 

Designs, - - - - - - 50 

Historic Ornament, - - - - "57 

Color, .--.-. 63 

Representative or Pictorial Drawing, - - - 69 

Paper Folding, ... ... ^5 

Clay Molding, - .... - 104 

Stick Laying, - ...... . 108 



INTRODUCTION. 



This book is intended merely as a bird's eye view of the 
snbject of industrial drawing as it is tanght in the public 
schools. It aims to aid the teacher in gaining a little know- 
ledge concerning each department into which the subject is 
divided. It does not claim to be even an attempt at cover- 
ing the ground in anything like a comprehensive way, but 
it will give the teacher a starting-point, at least, from which 
to pursue the subject in all its branches. 

While doing Institute work the author has been asked 
numberless times to designate some book which would give 
an all-round glimpse of drawing, and while there are many 
books treating of any one of the topics considered in this 
book, they are treated so comprehensively that the teacher 
is discouraged at the thought of the mass of material she 
must read to get what she really wants; and in order to know 
even a little of each of the topics to be considered she must 
read as many books as there are divisions of the subject, and 
it is this that has led the author to give this little book to 
the public, in the hope that the teacher may find in it the 
points in drawing which it is necessary she should know. 

It is often asked, "Why teach drawing in the public 
schools?" Drawing has long been looked upon as a merely 
ornamental study, and as such of little value from an educa- 
tional standpoint; but, at last, we have awakened to the fact 
that drawing as an accomplishment, is a very small part of 



VI INDUSTRIAL DRAWING. 

a very large subject, and we indicate this when we denomi- 
nate the subject as taught in the public schools, industrial 
drawing. 

The true aim of education is to cultivate the faculties in 
all directions, and drawing has been found to be a very im- 
portant factor in this work in the cultivation of observation, 
memory, imagination and imitation, and also in awakening 
the power and dexterity of the hand in the work of con- 
struction. 

It is of value, too, as a means of thought expression; it 
being possible to show at a glance by a drawing what could 
not otherwise be told except by lengthy description, and 
perhaps even then not adequately expressed. 

Drawing has been aptly called the "universal language." 
Learning to draw is learning to see, and the seeing must al- 
ways outrun the drawing. 

When any object is seen in its correct proportions and 
form it is easy to make a representation of it. 

One day a class of teachers were asked to make a memory 
drawing of a half-apple. The form was drawn without dif- 
ficulty, then came the question from one of the members of 
the class, "Which way do the seeds point, toward the stem 
or toward the bud?" Out of a large class but few were posi- 
tive in their knowledge on this point. We have found that 
many people, even among those who have spent a large part 
of their lives upon a farm, are uncertain whether a cow's 
horns are in front of, or behind the ears. 

One day a cube was shown to a class and the question 
asked "Do you really know the cube?" All thought they 



INTRODUCTION. VH 

undoubtedly did. The cube was then put out of sight and 
the class were asked "How many corners has the cube?" 
There was a visible eflfort to recall the image to memory, 
and after a moment's hesitation, while many answered cor- 
rectly, several could not tell the exact number. 

This ignorance is merely the result of not having been 
trained to habits of careful observation. 

"Seeing, we see not." 

Madame Cave says, "As soon as you see correctly, you 
feel correctly, you execute correctly. If you follow your 
eye, your observation, you will secure correctness, you will 
find truth, you will be natural, and naturalness is simply 
truth. This accuracy, this naturalness, is the result of much 
observation, of great memory." 

Rubens says, "To see, to understand, to remember, is to 
know." 

Besides its value as an educational factor in the training 
of the mind and eye, drawing is of little less importance as 
an educator of the hand. Man has been distinguished from 
all other animals by his manual dexterity; he is primarily a 
constructive being. This tendency which shows in the child 
at a very early age, finds a natural outlet in the work in 
drawing, especially in Geometric or Constructive drawing. 

A boy or girl who has had thorough instruction in indus- 
trial drawing has been given a much wider range from which 
to choose his life work. In towns where there is little manu- 
facturing the boy has almost no choice except between the 
store and the office, but if his mind has been awakened to 
that great field which drawing opens to him, he can choose 



Vill INDUSTRIAL DRAWING. 

the place for which he feels nature has fitted him. The girl 
who has energy and perseverance need no longer feel that 
the schoolroom or the office is the only place for her. The 
girl and the boy have the choice of the mechanic arts, archi- 
tecture and draughting; the decorative arts, designing, fres- 
coing, lettering; the plastic arts, modeling, carving, sculp- 
ture; and the reproductive arts, etching, engraving, litho- 
graphing and photography. 

Drawing as taught in the public schools, cannot, of course, 
give the pupil even an elementary knowledge of these 
branches, any more than the penmanship taught in school 
will give him a knowledge of business forms that would 
make him at once capable of filling a bank cashier's place, 
but it will train his mind, his eye, his hand, so that if he 
possesses some taste for drawing, and earnestness of purpose, 
and chooses to enter the industrial arts he will make his 
work a success. 

For the teacher, a knowledge of the elements of drawing 
and the ability to use the pencil or crayon graphically is of 
immense advantage. There is no branch of learning to 
which the teacher cannot apply it with advantage to the 
youngest as well as the oldest pupils. 

The time has come when the state has recognized the ne- 
cessity of teachers having some knowledge of drawing and 
has emphasized it by requiring them to pass an examination 
in this branch. The opportunities for the study of drawing 
have been very limited for teachers who have not had a pro- 
fessional training, and this little book is offered as an aid to 
assist them over some of the hard places and perchance to 
tempt them to a farther study of this fascinating subject, 



Industrial Drawing is divided into three departments: I. 
Constructive Drawing. II. Decorative Drawing. III. Pic- 
torial Drawing. 

I. Constructive, or Geometric Drawing includes the study 
of geometric definitions and problems, working drawings, 
and development of surfaces. 

II. Decorative Drawing or Ornament includes the study 
of plant forms, and their conventionalization, elementary de- 
sign, historic ornament, and color. 

III. Pictorial Drawing or Representation treats of the 
representation of objects when seen from one point of view. 



CONSTRUCTIVE 

OR 

GEOMETRIC DRAWING. 



GEOMETRIC DRAWING. 



I. GEOME'TRIC DEFINITIONS. 

A line has length only. There are three classes of lines, 
— straight, curved and broken. In drawing, a line is the 
picture of an edge or an outline. 

A straight line is the shortest distance be- 
tween two points. ■ 

A curved line changes its direction at every 
point. 

A broken line is made up of short straight 
lines. 

According to their direction lines are classed 
as vertical, horizontal and oblique. 

A vertical line is one which extends up and 
down toward the top and bottom of the page. 

A horizontal li^te is level, /. e. , it extends from 
left to right. 

An oblique line is one which slants. 

In their relation to each other lines are classed 
as parallel or at an angle. 

Parallel lines are those which run side by side 
and if extended indefinitely would never meet. 

Lines which would meet if extended are at 
an angle. 




13 INDUSTRIAL DRAWING. 

Lines which would meet at right angles are 
perpendicular to each other. (Note differ- 
ence between vertical and perpendicular.) 

An angle is the difference in direction be- 
tween two lines. 

(An angle is measured by degrees or parts 
of a circle, and not by length of lines.) 

The point of meeting of these lines is called 
the vertex of the angle. 

An angle opening 90 degrees, or a quarter 
of a circle, is a right aiigle. 

The lines of a right angle are always per- 
pendicular to each other. 

An obtuse angle is larger than a right angle, 
t. e.^ it has an opening of more than 90 de- 
grees. 

An aaite a?igle is smaller than a right angle, 
i. e.^ it has an opening of less than 90 degrees. . 



A plane figure is one having length and breadth, but no 
thickness. 

Plane figures may be either rectilinear, curvilinear, or 
mixtilinear. 

A rectilinear figure is bounded by straight lines. 

A curvilinear figure is bounded by curved lines. 

A mixtilinear figure is bounded by both straight and 
curved lines. 

(A semicircle is a mixtilinear figure.) 

The sum of the straight lines which bound a figure is the 
perimeter of the figure. 



GEOMETRIC DRAWING. 



13 



Rectilinear figures are divided according to the number of 
sides and angles, into three classes, triangles, quadrilaterals, 
and polygons. 

A triangle is a plane figure having three sides and three 
angles. 

Triangles are classified according to angles and to sides. 

According to angles, triangles are divided into three class- 
es: right-angled triangles, obtuse-angled triangles, and acute- 
angled triangles. 



A right-angled triangle is one having one 
right angle. 



An obtuse-angled ti'iangle is one having 
one obtuse angle. 



An acute-angled triangle is one having all 
of its angles acute angles. 

According to sides triangles are classed as 
equilateral, isosceles, and scalene. 

An equilateral triangle is one having three 
equal sides. 

An isosceles triangle is one having two of 
its sides equal. 




A scalene triangle is one no two of whose 
sides are equal. / ^^^^ 

All triangles may belong to one class of each division. 

A rectilinear figure having four sides and four angles is 



14 INDUSTRIAL DRAWING- 

called a quadrilateral and its angles may be either right, ob- 
tuse or acute. 

A quadrilateral having none but right angles and its op- 
posite sides equal, is a rectangle. 

There are but two rectangles, the square and the oblong. 



A square is a rectangle having all of its sides 
equal. 

An oblong is a rectangle having two of its 
sides longer than the other two. 

A parallelogram is a quadrilateral whose opposite sides 
are parallel but whose angles may be either right, acute, or 
obtuse. 

Under this head we have the rhombus, or rhomb, and the 
rhomboid. 

The rhoinbus.^ or rhomb^ has four equal sides / / 

but its angles are not right angles. / / 



The rhomboid is an elongated rhomb. It 
has two acute angles and two obtuse angles, ■ r 
and two of its sides are longer than the other >— 
two. 



A trapeziimi is a quadrilateral no two of 
whose sides are parallel. 

A trapezoid is a quadrilateral having only 
two of its sides parallel. 



GEOMETRIC DRAWINGS. • 15 

Rectilinear figures having more than four sides and four 
angles 2.x^ polygons. If the sides are equal, they are called 
regular.^ if unequal, irregular. 

A pentagon is a polygon having five sides and five angles. 

A hexagon has six sides and six angles. 

A heptagon has seven sides and seven angles. 

An octagon has eight sides and eight angles. 

A nonagon has nine sides and nine angles. 

A decagon has ten sides and ten angles. 

An nndecagon has eleven sides and eleven angles. 

A dodecagon has twelve sides and twelve angles. 

A circle is a plane figure bounded by a curved line every 
where equally distant from a point within called its center. 
A circle contains 360 degrees. 

The circumference is the line which bounds the circle. 

The diameter of a circle is a line 
which passes through the center of a 
circle and touches the circumference 
in two points. 

The radius of a circle is a line whichl 
passes from the center to the circum- 
ference and is always equal to one-half 
of the diameter. 

A chord is a straight line which cuts the circumference in 
two points but which does not pass through the center of 
the circle. 

An arc is the part of the circumference cut off by the 
chord. 




16 



INDUSTRIAL DRAWING. 



A semich'cle is the half of a circle. It con- 
tains 1 80 degrees. 

A qiiadrajit is the qnarter of a circle and 
contains 90 degrees. 

A segment is the space bonnded by an arc 
and a chord. 




A sector is a part of a circle bonnded by an 
arc and two radii of a circle. 



V^ 




An ellipse is a plane fignre bonnded by a 
regular curve every point in which is at the 
same combined distance from the foci. 

(A circle seen in perspective is an ellipse.) 

An ellipse has two diameters, a hug diameter and a short 
diameter. 

The long diameter is the longest straight line which can 
be drawn within the ellipse. It is also called the major axis 
of the ellipse. 

The short dia?neter is the shortest straight line which will 
cut the ellipse into two equal parts. It is called the minor 
axis. 

Foci are points in an ellipse from which the curve can be 
drawn mechanically. 



CrEOMETRTC DKAWIXCJ 



All oval is an egg-shaped figure. A semicir- 
cle combined with a half-ellipse will produce a 
very good oval, the radius of the semicircle be- 
ing one-third of the length of the major axis of 
the oval. 

The base of a f)lane figure is the line upon 
which it rests. 

The apex is the highest point above the base. 

The altitude is the perpendicular distance 
from base to apex. 

An axis is the straight line on which a bod}' 
revolves, and it divides it into two equal and 
similar parts. 

The diagonal is a line passing through the 
center and connecting opposite angles. 

The diameter is any line drawn through the 
center of a figure and extending to the center? 
of opposite sides. 

The center of a plane figure can be found by 
drawing the diagonals, the point of intersection 
being the center. 




18 



INDUSTRIAL DRAWING. 



A solid is that which has lenorth, breadth and thickness. 



A sphere is a solid bounded 
by one curved surface, every 
part of which is equally dis- 
tant from a point within called 
the center. 

A hemisphere is half a sphere. 

A spheroid is a nearly spher- 
ical body formed by the revo- 
lution of an ellipse upon one 
of its axes. If the ellipse is 
revolved upon its major axis, 
or long diameter, the prolate 
spheroid is obtained. 

This form of the spheroid is 
also known as the long spher- 
oid^ or the ellipsoid. 

If the ellipse is revolved 
upon its minor axis or short 
diameter, the oblate spheroid \z 
obtained. This solid is also 
called \\\^Jiat spheroid. 






The ovoid is an egg-shaped 



solid. 



GEOMETRIC DRAWING. 



A cylinder is a solid of roller-like form 
whose longest section is oblong and the cross 
section is circnlar. 




A half-cylinder is a solid formed by divid- 
ing a cylinder vertically in two equal parts. 
It has two semicircular ends. 



A cone is a solid tapering to a point from a 
circular base. 




A cube is a solid bounded by six equal 
square faces. 




A prism is a solid whose ends are similar, equal and par- 
allel, and whose sides are oblong. Prisms may be triangu- 
lar, square, pentagonal, hexagonal, or octagonal, according to 
their bases, but they must all have oblong 
sides. 



A triangular prism is one whose base?, 
are triang-les. 




30 



INDUSTRIAL DRAWING. 



There are two triangular prisms, the rightangled triangu- 
lai' prism^ which is formed by the division of the square 
prism on one diagonal of the bases, and 
the eqiii-triangular prism ^ whose bases are 
equilateral triangles. 

The square prism is one whose ends are 
square. 

A pyramid is a solid having either a tri- 
angular, square, or polygonal base, and 
whose sides are triangles, uniting in a point 
at the top. 

A square pyramid is one whose base is square and it has 
four triangular sides. 

A plinth is the lowest division of the base of a column. 
It is a short horizontal section of either a cylinder or a 
square prism. 

The circular plinth is the horizon- 
tal section of a cylinder. 





The square plinth is the horizontal 
section of a square prism. 

The frustum of a solid is the part 
next the base, formed by cutting off 
the top parallel to the base. 

A circular frustum is formed from 
the cone. 




A square frustum is formed from 
the square pyramid. 



GEOMETKIO DRAWING. 21 

The axis of a prism is a straight line connecting the cen- 
ters of the ends. 

The axis of a pyramid or cone is a straight line connect- 
ing the apex with the center of the base. 

The apex of a pyramid or cone is the highest point above 
the base. 



GEOMETRIC PROBLEMS. 



CONSTRUCTION OF SOME SIMPLE PLANE FIGURES WITHOUT 
THE USE OF COMPASSES. 



Prob. 




I, To construct an equilateral triangle. 

Draw the given base AB, find 
the center of the base, and draw 
an indefinite line perpendicular 
to this point. With the ruler 
take the exact measure of the 
base. Place the ruler upon A so 
that the number indicating the 
required length shall fall exactly 
upon this point, then turn the 
ruler until the end falls upon the 
indefinite line, taking care that the ruler does not slip from 
A. The point thus found upon the indefinite perpendicular 
will be the vertex of the triangle. Prove your work by 
testing the remaining side and then complete' the triangle. 

Prob. 2. To construct an isosceles triangle. 



Draw the base AB, and find the 
center. Draw an indefinite line 
perpendicular to the center of the 
base. On this line measure the 
given altitude and finish the tri- 
angle. 




GEOMETRIC PROBLEMS. 



Prob. 3. To construct a pentagon^ 

Draw a circle of the required size 
an ddivide it into five equal parts, by 
laying off an assumed fifth with two 
fingers or pencils and then judging of 
the other four divisions. 

Consulting the face of a watch or 
clock will aid materially in the solu- 
tion of tliis problem. Consider the 
hour to be divided into five portions 
of twelve minutes each, and the vertex to fall upon XII. 
Place dots where each division occurs and finish the penta- 
gon by connecting the points. 

Children may be aided in dividing circles into three or six 
equal parts, by the use of the clock face. 




Prob. 



4. To construct a hexagon. 

Draw a horizontal AB, equal to 
the extreme width of the desired 
figure. Divide AB into four equal 
parts and name the central division 
C. Consider AC to be the base of 
two equilateral triangles, one ex- 
^^ tending above AC and the second 
below AC. Proceed to draw as in 
Prob. I. Next consider CB to be 
the base of two similar triangles and 
construct them. To finish the 
hexagon join the vertices of the tri- 
angles by horizontal lines. 




24 



INDUSTRIAL DRAWING. 



Prob. 5. 



To construct an octago7i. 

Draw a square of the size of the 
desired octagon and draw its diago- 
nals. Take the measure of one 
semi-diagonal and lay off this dis- 
tance on the sides of the square, 
measuring from each corner in both 
directions. Join the points by ob- 
lique lines which cut off the corners 
of the square. 





Prob. 6. To construct an ellipse. 

- - 'T ""~~--^ Draw the long and short di- 

ameters of the desired length. 
\ Use a long narrow strip of pa- 

,' per to obtain points. Mark 

one end of the paper A. From 
A mark off one-half the short 
diameter and name this point 
S. From A mark off one-half 
of the long diameter and name this point L. Place this 
strip of paper on the drawing so that S shall fall somewhere 
on the long diameter, and L somewhere on the short diameter, 
and place a mark at A. This is one point in the circumfer- 
ence of the ellipse. Any number of points may be found 
in the same way. 

Through the points found draw the ellipse. 



Prob. 7. Another method 0/ drawing an ellipse. 

Drive two pins firmly into the paper any desired dis- 
tance apart. Knot a stout thread about the pins letting 



GEOMETRIC PROBLEMS. 



25 



the thread be somewhat longer than the distance between 

the pins. Hold the pencil 
point firmly against the line 
keeping it taut all the time 
and beginning at the left 
draw the upper half of the 
ellipse. Beginning again at 
the left, draw the lower half 
of the ellipse. 




Prob 




To construct an oval. 



Draw a vertical line the length of the 
desired oval and divide it into three equal 
parts, through the upper point of divi- 
sion draw a horizontal line two-thirds of 
the length of the vertical and use this as 
the base of a semicircle. Upon the low- 
er two-thirds of the vertical construct a 
half-ellipse using either method given in 
the two preceding problems. 



APPLICATIONS. 

Objects based on the square — Book, box, inkstand, envel- 
ope, flag. 

On the triangle — Bottle, kite, brush, signal flag, sail. 

On the circle — Fan, coins, watch, curtain ring, baseball. 

On the oblong — Box, book, envelope, house, door, win- 
dow, picture frame. 

On the ellipse — Eye glasses, picture frame, melon, potato. 

On the oval — Fan, acorn, ^^^^ horseshoe. 

On the octagon — Frame of clock face, silk reel. 

On the pentagon — Ivy leaf. 



INDUSTRIAL DRAWlNGf 



TO BE CONSTRtfCTED ACCURATELY WITH INSTRUMENTS. 

Prob. I. To bisect a straight line. 

Draw the given line AB. With a 
radius of more than half the line and 
A and B as centers, draw arcs that will 

intersect both above and below the 

■^ line in C and D. Join C and D. CD 
is perpendicular to AB and divides 

// the line AB into two equal parts. 

\ 

To bisect an arc proceed in the same manner as for a 
straight line. 
Prob. 2. To erect a perpendicjilar at the end of a given line. 

><^ Draw the line AB. With 

B as a center and any radius 
draw an arc cutting AB in C. 
With C as a center and the 
same radius draw an arc cut- 
ting the first arc in D. With 
D as a center and the same 
radius cut the same arc in E. 
With D and E as centers draw arcs intersecting in F. Draw 
BF which is the perpendicular required. 
Prob. 3. To bisect an ajigle. 

Draw the angle ABC. With A as 
a center and any radius draw an arc 
cutting the sides of the angle at B and 
C. With any radius greater than one- 
half the arc BC and B and C as cen- 
ters draw arcs intersecting at D. 
Draw AD which will bisect the angle. 





GEOMETRIC DKA WINGS. 



27 



Prob. 4. To constrtcci an equilateral triafigle on a give?i 
base. 



Let AB be the given base. With a 
radius equal to AB and A and B as cen- 
ters, draw arcs which will intersect in C. 
Connect AC and BC. ABC will be 
the desired triangle. 



To construct an angle equal to a given angle. 

Let BAC be the given angle. Draw 
any line as DE and take any point in it 
as D. With A as a center and any radi- 
us draw an arc which will cut the sides 
of the given angle in B and C. With 
D as a center and the same radius, draw 
an arc that will cut DE in E. Take a 
radius equal to BC and with E as a cen- 
ter cut the arc EF in F. Join DF and 
EDF is the desired ansfle. 




To trisect a given 7'ight angle. 



Let ABC be the given right angle. 
With center B and any radius draw an 
arc that will cut the sides of the angle 
in A and C. With the -same radius 
and A as a center cut the arc AC in D. 
With C as a center and the same radi- 
us cut the arc AC in E. Join B and 
E and B and D. 



28 



INDUSTRIAL DRAWING. 



Prob, 6. To constr2ict a square on a given base^ AB. 



Erect BC perpendicular to B 
according to Prob. 2. Take a 
radius equal to AB and with B as 
center cut BC the same length as 
AB. With the same radius and 
A and C as centers draw arcs that 
will intersect in D. Draw AD 
and CD. 




Prob. 8. To construct a regular hexagon on a given base. 

Let AB be the given base. With 
a radius equal to AB and A and B 
as centers draw arcs intersecting in 
^C. With C as a center and the 
same radius draw a circle passing 
through A and B. With B as a 
center and the same radius cut the 
circle in D. With D. as a center 
and the same radius cut the circle 
at E. With E as a center and the same radius cut the 
circle at F. With F as a center and the same radius cut the 
circle in G. Join BD, DE, EF, FG, and GA. 




Prob. 9. To construct a regular pentagon on a given base^ 

AB. 

With a radius equal to AB and A and B as centers draw 
two circles intersecting in C and D. Join CD. With D 
as a center and a radius equal to AB draw an arc which 



eSOMETEIC PROBLEMS. 



29 




will cut the left circle in 
E and the right circle in 
F and the line CD in G. 
Join E and G and extend 
the line till it will cut the 
right circle in H. Join 
\ F and G and extend the 
line till it cuts the left cir- 
cle in K. With a radius 
equal to AB and H and 
K as centers draw arcs 
that will intersect in L. 
Draw BH, HL, LK, and 
KA. 



Prob. I( 



To construct a 7'egiilar octagon on a given base. 

Let AB be the given base. 
Erect perpendiculars at A 
and B (Prob. 2) and extend 
AB indefinitely to the right 
and left. Bisect the exterior 
right angles at A and B (Prob. 
3). Make the bisecting lines 
AC and BD equal to AB. 
Draw the line CD cutting the 
perpendiculars in E and F. 
From E and F lay off dis- 
tances EG and FH equal to 
AB. Through GH draw an 
indefinite line. Make GK, GL, HM, and HN each equal to 
AE or BF. Draw BD, DN, NM, ML, LK, KC, and CA. 



k/~ — ■ ^ ^ _Y 



WORKING DRAWINGS. 



Working drawings are made to assist the artisan in con- 
structing any manufactured object. They are in no sense 
pictures of the objects, but are simply statements of the /ac/s 
to be considered, that is, they indicate the length, width and 
height of the object to be made, together with the size and 
position of all its parts. 

In order to show the three dimensions more than one view 
uf the object must be drawn, and the number of the views 
is limited only by the simplicity or intricacy of the object 
under consideration, however, three views are usually suffi- 
cient to show all necessary facts of simple objects. 

The "front view" is usually drawn first, and this view 
must represent not only the outline of the object, but all the 
edges that modify the front, and will include everything that 
can be seen when looking at the object directly in front. 



Fig. I shows the front view of a cube. 



If the cube had a cylindrical hole through it, 
it would appear as in Fig. 2. 




WORKING DRAWING. 



31 



If a cubical inkbottle were represented the 
neck would appear as in Fig. 3. ' ^-^^ 




The "top view" will show only what can be 
seen in looking down upon an object from above 
and must include everything that can be seen 
from that point of view. 

Fig. 4 represents the top view of a cube. 



Fig. 5 shows the top view of a cone. 

Pupils often confound the two terms "top" and 
' 'top view' ' and think the point the top view of a ^. 




Fig. 7 shows the top view of the square pyra- 
mid. 




9^7 



It must be remembered that zither ever there is ait edge 
there nnist be a line. 

Sometimes an end or side view may also be necessary, and 
this will include only what can be seen by looking at the ob- 
ject from that side. 



INDUSTEIAL DRAWING. 



If the article is hollow, or there is some interior mechan- 
ism, it may be necessary that the interior be shown. This 
is done by making a "sectional view." The section usually 
assumes the object to be cut by either a vertical or horizon- 
tal plane. 

The section is cross-hatched to indicate the 
cut through the solid portion of the object. 
Cross-hatching is done by drawing parallel ob- 
lique lines about one-eighth of an inch apart 
across the cut portions. The lines may slant in 
either direction. 



Fig. 6 shows a section of a hollow cylinder. 



i 
i 

i 




i 



Sometimes the top view is drawn above the front view and 
sometimes below it. According to the principles of ortho- 
graphic projection it should be drawn below the front, but 
many draughtsmen prefer to give it its own place, and practic- 
ally, it is of no consequence whether it is placed above or be- 
low, if the views are all properly marked so there may be no 
danger of confusion. It is necessary, however, to have the 
views stand in such relation to one another, that points may 
be connected to show their relative position. 

There are five kinds of lines used in working drawings. 

Dot-and-dash lines are center lines. They are sometimes 
called construction lines. 

Full lines represent visible edges and outlines. 

Dashed lines represent invisible edges. 

Dotted lines connect views. 



WORKING DRAWING. 



Light lines, arrow-points, and figures indicate measure- 
ments. 

It is not necessary to use center lines unless the object has 
a curved outline or is difficult to illustrate. 



Unseen edges are shown upon 
corresponding views. This is illus- 
trated in Fig. 7, the working draw- 
ing of the spool. It will be seen 
by examining a spool and compar- 
ing it with this working drawing 
that every fact is clearly told. The 
hole through the spool does not 
show when the spool isviewed from 
the front, but its presence is indi- 
cated by dashed lines, which are 
connected by dotted lines to the top 
view of the hole which is a small 
circle. It will easily be seen that 
this is the only way in which the 
hole could be shown in its true 
length except by a sectional view. 
It will also be noticed that the cir- 
cle representing the shape of the 
"shank" of the spool is indicated 
in the same way upon the top view. 




^^7 



34 



INDUSTRIAL DRAWING. 



Fig. 8 gives the working drawing of the 
sphere and the necessary measurements. 

All measurements should be carefully 
placed on the drawing. The arrow-points 
are to be made freehand and must indicate 
the entire length of the distance measured. 
This must frequently be indicated by "ex- 
tension" lines as shown in Fig. 8. The 
measurement lines must have a little space 
left in the center for the figures. 

The figures must always read from left 
to right, and from top to bottom. The 
opening of the arrow-heads must be toward 
the figures. 

Two small dashes placed at the upper 
right corner of the figure indicate inches, 
thus, ']" is read "seven inches." 

One small dash in the same position in- 
dicates feet, thus, 6' is read "six feet." 

6' ']" means "six feet and seven inches." 

The top view or the bottom view is often 
called the "plan." 

The side view or the front view is known 
as the "elevation." 

Architects always use the terms "plan" and "elevation." 

Fig. 9 shows a working drawing of a cube. Notice that 
here as in Fig. 8 the measure of the width is placed between 
the two veiws as it is a measure common to both of them, 
and it is best to show measurements in as few places as 
possible. 




WORKING DRAJVVINGS. 



35 




Fig. lo is the working drawing of a square prism, using 
one of the oblong faces as the front. 

Fig. II shows a working drawing of a square prism turn- 
ed at an angle of 45 degrees. Notice that the measures in 
the top view are placed upon the oblique edges these being 
the true measures of the prism, but the width of the oblongs 
is not given as this can be determined only by the diagonal 
of the top. 

Fig. 12 is a working drawing of the square prism when 
placed at an angle of 30 degrees to the right. It will be ob- 
served that the farther corner of the top does not coincide 
with the nearer angle, and if the prism were transparent, 
the back edge would be seen, it is therefore indicated by 
dashed lines. 



INDUSTRIAL DRAWING. 



' 3 I, 




Fig. 13 is a working drawing of the square pyramid. 
Notice the manner of indicating the measure of the altitude 
of the triangle. It is well to put most measurements out- 
side of the drawing and, wherever possible, to the left of the 
drawing. 

Fig. 14 is the working drawing of the ellipsoid. 

In giving measurements of circles the diameter should al- 
ways be given and not the radius. 

Fig. 15 is the working drawing of a right-angled trian- 
gular prism. Notice that the length of the front and side 
views is indicated by a measurement placed between the two, 
and that the width of the side view is not indicated, because 
it is determined by the hypothenuse of the top view. 



WORKING DRAWINGS. 



37 




. ^-r-^ . 




1 1 1 

1 
1 ' 1 

II : 1 



i i 



Fig. i6 is a working drawing of a washer. In fractional 
measurements the fractions should always be reduced to the 
lowest terms and the dividing line of the fraction should be 
horizontal rather than oblique, thus, "one-half" should be 
written ^ not ^. 

Fig. 17 shows the working drawing of a hollow cylinder 
with a sectional view. 

Working drawings should first be drawn freehand, and af- 
terwards from the freehand sketch an accurate drawing be 
made, using all necessary instruments both for drawing an4 
measuring. 



38 INDUSTRIAL J)EA WING 

DEFINITIONS OF TERMS USED. 

A working drawing is a drawing from which an object 
may be accurately constructed. 

Front Elevation — What can be seen when the front alone 
is observed. Front view. 

Side Elevation — What can be seen when one side is ob- 
served by itself Side view. 

Plan — What can be seen when looking directly down upon 
the object. -Top view. 

Sectional View — The representation of an object as it 
would appear if cut through by an intersecting plane. 



DEVELOPMENT. 



The tinsmith, the shoemaker, the glovemaker, and many 
other craftsmen, must use patterns in their work, the pattern 
being a drawing of the entire surface of the object, which, 
if folded together, and fastened, would form a complete 
model of the object. 

These patterns are called developments or flats. 

It is absolutely necessary that a development should be of 
accurate size and that the parts should be correctly adjusted, 
in order to match when folded together, therefore all work in 
the flat must be done with a luler and carefully measured. 

The development must be drawn with clear bright lines, 
and the laps for fastening, with light lines. 

Laps should not be placed on the top or base but on the 
sides of the object. They should be about y^" in width, 
and carefully bevelled at the corners so they will not inter- 
fere with each other when the object is folded together. 

Fig. I shows the development of the cube. 











/ \ 


/ \/ \ 










\ / 






\ J 







40 



INDUSTRIAL DRAWING 



Fig. 2 is the development of the square prism. 













/■ \ 


/ \/ -\ 








/ 


k / 




J. _J. 





Fig. 3 shows the development of the square plinth. 













/ \ / \ 










X / 




\ / 


\ / 




J^s 



DEVELOPMENT. 



41 




Fig. 4 shows the development of the triangular prism. 

By experiment- 
ing a littleL'with 
the development 
'of these simple ge- 
ometric solids it 
will be seen that 
many pretty and 
convenient arti- 
cles may be con- 
structed by slight 
changes in these 
fundamental de- 
velopments. 

Boxes of various shapes, card cases, match safes, and many 
other pretty little articles can be easily made. 

Fig. 5 is the development of the square pyramid. 

To draw this de- 
velopment take a ra- 
dius equal to one of 
the long sides of a 
triangular face of a 
pyramid and draw an 
indefinite arc using 
A as a center. Join 
A and B. Take a 
a radius equal to one 
side of the base and 
with B as a center 
cut the arc ni C With C as a center and the same radius 
cut the arc in D. With D as a center cut the arc in E. 




42 



INDUSTRIAL DRAWING. 





>Lr 6 



With E as a center cut the arc in F. Join AC, AB, AD, AE, 
and AF. Draw the chords to the arcs BC, CD, DE, and EF. 
On the side CD draw the base of the pyramid. 

Fig. 6 is the develop- 
ment of the hexagonal 
prism. 

A knowledge of the 
geometric problems given 
in another part of this 
book will be of great as- 
sistance in working out 
many of the more intri- 
c a t e developments, i n 
fact, it would hardly be 
possible to do the work 
with any degree of accur- 
acy without them. 
Fig. 7 shows the development of the cylinder. 

In the development of 
objects having circular 
faces like the cylinder, 
cone, etc., the approxi- 
mate length of the strip 
for the side may be gained 
by multiplying the diam- 
eter of the circular face 
by 3. 1 41 6, but if accurate 
work is desired resort 
must be had to the com- 
passes. 

With the aid of the com- 
passes draw a circle the 




DEVELOPMENT. 43 

size of the end of the desired cylinder. Quadrisect the cir- 
cle, bisect one of the quadrants, bisect one of the half-qnad- 
rants, and then bisect one of the last divisions. Draw the 
chord to the last arc and it will be very nearly 1-32 of the 
entire circumference. If the circle is a very large one it 
would be well to subdivide still farther, but for a 2" circle 
the variation between the chord and the arc of 1-32 will be 
too small to affect the accuracy of the work when finished. 

Laps for objects having curved surfaces should be wedge- 
shaped, and separated far enough so they will not overlap. 

The development should be usually made from a working 
drawing, so that the working out of geometric problems may 
appear in the drawing but not in the development. 



AI.PHABET. 

The alphabet gi\en below is peculiarly adapted to mechan- 
ical drawing as the letters are made up entirely of straight 
lines and therefore the letters may all be made with a ruler 
if desired. 

/\\hL\]LV[:,\\\l\LN\{i 
/7PQf^5T[]^M/xy Z 



DECORATIVE DRAWING 

OR 

ORNAMENT. 



BOTANICAL DRAWING. 



Botanical Drawing includes all study of plant form, and 
must precede all work in design except that of the simplest 
form, i. e.^ designs composed of geometric forms. 





h' 



The drawing of entire edged leaves comes first in this 
work and after this, the drawing of serrated leaves, and fin- 
ally lobed and compound leaves. Much interesting work 
may be done in the drawing of pods, acorns, peanuts, beans, 
peas, corn, etc. 

In leaf drawing consider the slant, general curve and 
length of the midrib and draw it, then determine the width 
of the leaf If the leaf is a simple one it can be drawn di- 
rectly, if it is lobed it should be "blocked in," i. ^., the gen- 
eral masses outlined and then the details of form drawn, (Fig. 
I.) Avoid drawing too many of the small veins, only enough 
of them being drawn to indicate the general growth. 



48 



INDUSTRIAL DRAWING, 





Good form and deli- 
cacy of treatment are 
essentials. 

In drawing sprays of 
leaves close attention 
must be paid to the 
growth of the leaves 
upon the stem, wheth- 
er opposite, alternate, whorled or perfoliate. 

All peculiarities of growth must be carefully noted and espe- 
cially the plac- 
ing of the leaf 
upon the stem. 
Make your 
leaves grow 
from the stem, 
do not make 
them look as 
if glued on. 

In the study of flowers choose for the first attempts very 
simple ones, as the wild rose, buttercup or apple blossom. 




h'- 





BOTANICAL DRAWING. 



49 



Draw them full face view and notice carefully the placing 
of the petals, whether overlapping, or not. Some flowers 
are easily drawn if studied from a side view, and under this 
head we find the violet and tulip. 

For the purposes 
of decoration, it be- 
comes necessary, that 
foliage and flower 
forms shall be shorn 
of their imperfec- 
tions, and that un- 
important details shall be either omitted or simplified; this 
change in form is known as conventionalization^ a conven- 
tional leaf being a modified form of the natural leaf that 
will adapt it to ornamental purposes. Figs, i, 2, and 3 are 
examples of natural leaves and their conventionalizations. 
For borders, vines may be made conventional, for rosettes, 
flower forms like the wild rose and daisy. Fig. 5. 




DESIGN. 



Ornamental design applies to the whole subject of decora- 
tion, and we must do as all nations before us have done — go 
to nature for our laws and principles. 

The principle which the child can most easily grasp is 
repetition. Anything which is repeated regularly, and at 
intervals, becomes pleasing to the eye, as intending design. 
Circles, squares, and other geometric figures, repeated regu- 
larly, form a pleasing border, and among the first ornaments 
of savage tribes were rows of shells, and we find the uncivi- 
lized races of today wearing 
strings of animals teeth, 
and with their dress deco- 
rated in angles to represent 




them. 



'^' 



Even a straight line be- 
comes ornamental when re- 
peated and is often used as 
a decoration for the dress of 
today. 

We get from the ancients 
many examples of simple 
repetition of lines, and it is 
possible that this was first 
suggested by reed plaiting. 
Figs. 2,3, and 4 are borders 
from Egyptian costumes. 



Fig. 5 is a Greek fret, 
and Fig. 6 is from the Chi- 
nese. 



Geometric figures were 



[__] C_-_Z1 [__] ni 1 o^^^^ ^s^^ i^^ ancient orna- 



ment. 



'7' 






Fig. 7 is an example of 
^ simple repetition taken from 



v/;//;//?;/^//////// //y////////////////iy an Kgyptian tomb. 



The next principle to be considered is alter natioit. Under 
this head we have four points to consider, alternation of po- 
sition, of form, of size, and of color. Alternation of posi- 
tion may have been ^rst suggested by the accidental mis- 
placement of the unit of design. Fig. 5, given above, is a 
good example of this principle in the fret. 



000: 


Vf 


VavaVavaVaV/ 



Figs. 8 and 9 are al- 
so simple illustrations 
of this principle. 



Z,.f 



52 



INDUSTRIAL DRAWING. 



V/////////////////////////////////777m 



'y////////////////////////?/////////7777777^^ 
1 



Fig. lo is taken from 
Byzantine jewel work. 

Alternation of form 
is illustrated in Figs. 
II, 12, and 13. 



UO)Dc:>DQn 



Fig'. II is taken from 
a Greek vase. 



Fig. 12 from an Egyp- /oVoVoVoVoVoVoVovB 
tian tomb. — -^=- ^^ 



Fig. 13 is the Greek 
astragal or bead mould- 
ing. 



/^./, 



J)0Q0Q0Q0Q ^l'°«"' i" Fig^- '4 and 



Alternation of jz^*? is 
15- 



nnDaDDDD 



^P?. 



Fig. 14 is a form of the 
Greek guilloche. 



Fig. 15 is an example of 
Byzantine jewel work. 



Great care must be taken in working out the next step, 

that pf aUernaUon 9f color. Until colpr has been made a 



53 



Study, designs should be worked out very cautiously and it is 
best that but one color should be taken, making a tint alter- 
nate with a shade, a tint with the standard, or a shade with 
the standard. 

The principles which apply to borders are equally applica- 
ble to radial arrangements or growth from a center. This 
form of ornament is also known as the rosette. As we get 
the idea of the border from the vine, so we receive the idea 
of radiation around a center from the flower, whose petals, 
sepals and stamens, all follow a regular arrangement about a 
center. (See Fig. 5 under Botanical Drawing.) 

Simple but beautiful examples of this, are found in the 
trefoil and quarterfoil. Figs. 16 and 17 are radial arrange- 
ments enclosed in the square. 




oS../. 




Radial arrangements must always have centers which will 
hold the radiating units firmly together, strength being one 
of the underlying principles of correct design. 



Radial arrangements may consist of any number of units, 



54 INDUSTRIAL DRAWING. 

and the enclosing form may be any geometric fignre, from 
triangle to a circle. See Figs. i8, 19, and 20, 






This principle of radiation may be carried still fnrther and 
the design radiate from a point, from a vertical line, or from 
a horizontal line. The Greek anthemion illustrates radiation 
from a point. The growth of leaves from the parent stem 
illustrates radiation from a line. Of symmetry in design, 
Leland says, "i^ny design, however meaningless or irregular, 
becomes s}'mmetrical as a part when it is accurately repeated 
in union with itself" Ward in his ''Principles of Orna- 
ment" says, ''The most unsliapen or ragged blot, if exactly 
reproduced on the opposite side of a straight line will make 
ornament, and at the same time illustrate symmetry." 

The law oi fitness or adaptation is by many writers placed 
as the primary principle of design, and it is that quality 
which makes the design in every particular adapted to the 
purpose for which it is used, and if added to or changed in 
any way would detract from its beauty. 

Contrast can be obtained both in form and color. We find 
examples of contrast of form in Figs. 11, 12, and 13. 

Repose is that quality in design that makes it restful to the 
eye. A wall paper that keeps the eye wandering from one 
part of the pattern to another, lacks this vital principle. 

A surface pattern is any design that repeats itself in the 
four directions. Under this head we have designs for wall 



paper, oil-cloth, textile fabrics, etc. The simplest surface 

patterns are made by repeating geometric units at regular 

intervals. 

Figure 21 is a simple 
illustration of the sur- 
face pattern. 

For use in borders 
and surface patterns, 
the simple geometric 
units may be modified 
by changes in the out- 
line of the figure with- 
out altering the gen- 
eral shape. 
By covering the "field" in such a way that the interstices 

also form pleasing shapes, very beautiful designs are obtained. 





B 




l^JXA^SIAj^ 



^7" 



Figs. 22, 23, and 24 are examples of modified squares. 
Fig. 23 is a Gothic unit. Fig. 24 is an example of Japanese 
enamel. 




Figs. 25 and 26 are ex- 
amples of modified tri- 
angles. 



56 INDUSTRIAL DRAWING. 

Modified circles are frequently based on flower forms and 
an example is seen in Fig. 5, Botanical Drawing. 

In all design it is necessary that due attention be paid to 
the distrilmtion of the units, i. e.^ they must be evenly placed 
on the surface to be covered, and they must be of such pro- 
portionate size of the entire field, that at least one-fourth of 
it is left uncovered. In surface patterns, the design should 
be so drawn that if the paper were rolled like a cylinder the 
pattern would match at the edges. This should be true of 
both directions. Sometimes, to add force and brilliancy to 
a design, it is necessary to half-tint the field or background, 
this will also add repose to the design by showing at once 
what the unit is, which the designer had in mind. 

Half-tinting is produced by drawing light fine parallel lines 
across all portions of the field uncovered by tlie design. 
Usually oblique lines are used, but this is not arbitrary. 
These lines should always keep the same direction over the 
field and never seem to radiate from the center. 



HISTORIC ORNAMENT. 



Historic Ornament embraces the ornament ot the various 
nations from the earliest tifnes. 

By reason of distinguishing characteristics, Historic Orna- 
ment is usually divided into six schools or classes, Egyptian, 
Grecian, Roman, Byzantine, Saracenic and Gothic. The 
three former belonging to the period of ancient history, and 
the three latter to that of medieval history. 

From the very earliest period of ornamental art, people 
have gone to nature for suggestions for decorative design, 
and from nature they have received the laws of their appli- 
cation. 

Now while all nations have gone to nature for their art, 
they have at the same time conventionalized all nature, that 
is, they have applied only the general laws of nature, and 
each nation has had its own individuality in its treatment of 
nature. This individuality has giv^en rise to the different 
schools of art and it has been modified by religion, state of 
refinement, and intercourse with other nations. 

Naturally, we find the simplest forms in the earlier days of 
art, for each nation has drawn from and added to its prede- 
cessor. We can easily recognize where the Greeks drew 
from the Egyptians, the Romans from the Greeks, and all 
succeeding art from all of these. In the ancient schools the 
Egyptian was mainly a symbolic art, while the Greek and 
Roman were purely aesthetic. 



INDUSTRIAL DRAWING 



The most important symbols in Egyptian art are the wave 
scroll of the Nile, the lotus, the papyrus, the winged globe, 
the asp, the fret, the beetle, and the cartouche containing 
hieroglyphics. 

The lotus, or water lily of the Nile, was the type of the 
inundation of that river, from which it obtained its fruitful- 
ness. The Egyptian priests taugl\t that a god dwelt in the 
lotus, and the more it was worshiped the more plentiful the 
harvest would be. The flower made its appearance just as 
the grain was coming out of the ground, and if large num- 
bers of loti were seen, the people believed they were to have 
a plentiful harvest. 

The lotus when used in or- 
nament, signified food for the 
body. Fig. i shows the nat- 
ural and the conventional lotus 
flower. 

The zig-zag or wave 
scroll of the Nile ap- 
peared very frequently. 
In its simplest form, it 
is composed of straight 
lines (Fig. 2) and is 
called the zig-zag. In 
its later form it is form- 
ed from the spiral 
(Fig- 3)- 

The papyrus grew in large triangular groves on the banks 
of the Nile, the apex of the triangle pointing towards the 




V- 



HISTORIC ORNAMENT. 



water. This peculiar growth, aided by the triangular shape 
of the blade, assisted it to withstand the great force of the 
current of the river. In the earliest times these plants were 
gathered, dried in the sun, and bound in great masses with 
cords and used for the construction of the people's huts. 
When architecture became a study they gave the convention- 
al treatment of this plant an important place. It was the 
type of the column with its capital, the flowers forming the 
capital, the stalks the column, the roots the enrichment of 
the base. These columns were arranged in long rows to 
typify the natural grove. The papyrus symbolized food for 
the mind. 



Often the column was covered with hiero- 
glyphics, sometimes in vertical and sometimes in 
horizontal rows. 



Fig. 4 shows the capital from a small column 
from the Temple of Luxor, dating 1250 B. C. 
It represents eight buds of the papyrus bound 
togrether. 



The winged globe 
(Fig. 5)]_was^'a talis- 
man of good luck. 
The globe represents 
the sun, the wings, Providence, and the two asps, power or 
monarchy. It was invariably placed over doors or windows, 
or in passages, and was sometimes of great size. 

The fret, shown in Fig. 6, is a symbol of Lake Moeris 





i..^ 



INDUSTRIAL DRAWING. 



with its twelve palaces and three thousand chambers, which 
typified the twelve signs of the zodiac and the three thou- 
sand years of transmigration which the wandering spirit was 
to undergo. 




/^.^. 



Grecian art was entirely aesthetic, that is, it was chosen 
wholly for its beauty, simplicity of form and adaptation to 
the object to be ornamented, and utterly without reference 
to any symbolism. The early period of Greek ornament 

was characterized by the echi- 
nus, the anthemion, the fret 
and the astragal. The echi- 
nus, sometimes called the ^^egg 
and tongue" moulding, was 
probably suggested by the 
Egyptian moulding contain- 
ing the oval and the pendant 
lotus. 



No. I, Fig. 7, is the Gre- 
cian form, and No. 2, Fig. 7, 
is the Egyptian. 




''r' 




HISTORIC ORNAMENT. 



61 



Fig. 8 is an illustration of the fret, many varieties of 
which were used. 



[^PP'^fp] 



7 

The Romans in their art merely elaborated Greek orna- 
ment. The only important element which they introduced 
was the arch, and while the Greeks used the scroll and the 
acanthus to a very limited extent, the Romans made them 
powerful factors in their ornamentation. 

The use of the arch opened a new field of architecture 
and this combined with the art of vaulting, which they 
learned from^the Etruscans, enabled them to cover in large 
spaces which the Greeks could not do. 




The Byzantine was the first Christian school of art and it 
was largely symbolic. Both in this school and the Gothic, 
geometric forms played an important part in design, for it 



C3 INDUSTRIAL DRAWING. 

was by these forms that they sought to teach the doctrines of 
the Christian faith. The circle symbolized eternity. Three 
interlaced circles, or the trefoil, (Fig. 9) signified the equal- 
ity and the eternity of the Trinity, the quarterfoil^ (Fi§'- 10) 
typified the four Evangelists. 

The serpent figures largely as symbolic of the Fall of Man. 
The cross occurs in almost all decoration and the cross is 
sometimes composed of five circles, the one in the center 
meaning the L-ord, and the four outer ones forming the quar- 
terfoil and referringf to the four Evangelists. 



COLOR. 



l^he teacher who wishes to make a study, however slight, 
of color, should provide herself with a glass prism of some- 
sort. A glass lamp pendant or paper weight will do if noth- 
ing else can be had, for no satisfactory work can be done un- 
til something is at hand whereby the colors of the spectrum 
can be obtained. 

It will first be noticed that red appears at the bottom of 
the spectrum but.it is usually the first color studied, because 
more familiar than violet which appears at the other end. 
The spectrum colors are six in number, red, orange, yellow, 
green, blue, and violet. The spectrum colors are also called 
the standard colors. 

Some writers have in past times given seven colors as the 
number, putting indigo between blue and violet, but modern 
scientists consider indigo as a mixture of blue and violet and 
drop it from the list. 

Interspersed with the standard colors there are innumera- 
ble hues, or mixtures of these colors, and by studying the 
hues, we get a prism of eighteen tones, namely: 

Red, Green, 

Orange Red, Blue Green, 

Red Orange, Green Blue, 

Orange, Blue, 

Yellow Orange, Violet Blue, 

Orange Yellow, Blue Violet, 

Yellow, Violet, 

Green Yellow, Red Violet, 

Yellow Green, Violet Red. 



64 INDUSTRIAL DRAWING 

The last hue, violet red, properly belongs to the begin- 
ning of the spectrum, 

A little thought will show how this spectrum has been se- 
lected, that is, if a little orange is mixed with a large pro- 
portion of red, we still have red, though it is no longer pure 
red but a hue of red, orange red. 

All the intermediate tones are composed in the same way. 

A mixture of two colors produces a hue, and a glance at 
the name of the hue will give the- predominating color, as 
well as the name of the one united with it. A sample book 
of colored papers such as may be had of dealers in art sup- 
plies for schools will be of great help at this point. By a 
little practice with these papers, some valuable facts may be 
ascertained. Take a piece of colored paper, some one of the 
standards is preferred, and hold it first in a strong light and 
then in a feeble light and note the changes which occur. It 
will at once be seen that the strength^ or valiie^ of a color 
changes in direct proportion to the brilliancy of the light it 
is subjected to. 

Red will vary from pink to brown, and these changes in a 
color according to the amount of light received are called its 
tones^ and these tones in regular order from the lightest tone, 
or brightest illumination, to the darkest, or entire absence of 
light, form a color scale. 

By mixing light, or in pigments, white, with a standard 
color, we obtain a tint of the color. 

By absence of light, or by mixing black with a standard, 
we obtain a shade of the color. 

Five tones will be sufficient for the ordinar}^ scale which 



COLOR. 65 

will be formed as tollows: i. Lightest tint; 2. Second tint; 
3. Standard color; 4. First shade; 5. Darkest shade. 

The first three colors iu the spectrnm, red, orange and yel- 
low, are often spoken of as ivarm colors, and the last three, 
green, blue and violet, as cold colors. 

Two colors which when mixed will produce gray are com- 
plementary to each other. 

The following are some of the pairs of complementary 
colors : 

• Red — Blue-green. Green — Violet-red. 

Orange — Green-blue. Blue — Orange-yellow. 

Yellow — Violet-blue. Violet — Green-yellow. 

While it is usually considered that complementary colors 
are harmonious, the colors should not be used in their full 
strength as this produces too harsh a combination to be pleas- 
ing. It is well to combine a tint of one with a shade of the 
other, or tints or shades of one with the standard of the 
other. 

Two colors are said to be harmonious^ if when placed side 
by side they form a pleasing whole. 

The simplest harmony is called dominant harmony^ and is 
composed of different tones of the same scale. Another 
harmony which may be classed under the same head is the 
combination of black, white and gray. 

Analogons harmony is produced by the combination of 
tones from neighboring scales. 

Complementary harmony is produced by the combination 
of colors which when mingled produce white. 



bb INDUSTRIAL DRAWING. 

The harmony of contrast is produced by the use of a color 
with black, white or gray. 

Owen Jones in his "Grammar of Ornament" gives some 
general principles concerning colors, which are appended: 

1. Color is used to assist in the development of form, and 
to distinguish objects, or parts of objects from one another. 

2. Color is used to assist light and shade, helping the un- 
dulations of form by the proper distribution of the several 
colors. 

3. When two tones of the same color are juxtaposed the 
light color will appear lighter, and the dark color, darker. 

4. When two different colors are juxtaposed, they receive 
a double modification; first, as to their tone, (the light color 
appearing lighter, and the dark color appearing darker) : 
secondly, as to their hue; each will become tinged with the 
complementary color of the other. 

5. Colors on white grounds appear darker, on black 
grounds, lighter. 



PICTORIAL DRAWING 

OR 

REPRESENTATION. 



REPRESENTATIVE OR PICTORIAL DRAWING. 



In pictorial drawing all objects are drawn simply as they 
appear, and not as they really are, that is, we do not draw 
the parts of an object in their true proportion one to another, 
but only in the proportion which they appear to bear to one 
another. As a consequence of this we cannot take measure- 
ments with a ruler as we do in mechanical drawing but we 
must depend very largely on the accuracy of our eye in find- 
ing apparent proportional measurements. 

But until we have trained our eye, by long and careful 
work, we must have other aid, and this help conies to us by 
means of the pencil. 

First determine the part of the object which is seen most 
nearly in its true size. Use this edge as the standard by 
which to measure other edges. 

Let the pencil be held with the fingers, leaving the thumb 
free to mark distances on the pencil. For measuriifg take 
care to use the top of the pencil, and not the point, 
and it must be held at artii^ s length so that there 
may be no change of radius. 

For level distances the pencil must be held ex- 
actly horizontal, for all vertical measurements it 
must be held perpendicular to the floor. When 
the measurement of the nearest edge is gained, 
■^^./. compare all others with it. 

For retreating distances like the top of the cube in front 




70 INDUSTRIAL DRAWING 

of and below the eye, hold the pencil in a vertical position, 
let the top of the pencil coincide with the farthest edge, 
place the thnmb at the point on the pencil where the nearest 
edge seems to come and without changing the position of the 
thnmb move the arm, till this apparent distance can be com- 
pared with the apparent height of the edge which is to be 
considered as a standard of measurement. 

It will be well to practice at first on large forms or plane 
figures, like the panels of a door or the panes of glass in a 
window. For practice at first, place yourself directly in 
front of the object to be measured and then verify the pro- 
portions gained by means of a ruler. Draw large quadrilat- 
erals upon the blackboard or cut them from paper and pin 
upon the wall and measure proportions. When you have ac- 
customed yourself to the use of the pencil for these meas- 
urements and feel that you can judge them accurately, change 
your sitting position to the left or right of the object, so. that 
you will see it obliquely, and take measurements again, and 
notice how the figure apparently diminishes in width hori- 
zontally. View the same object from all possible points and 
note rejy.ilts. The time spent in this way will be of great 
advantage in training the eye to see correctly; 

For measuring angles two narrow 
strips of board, cardboard, or paper 
may be used. If paper is used it 
must consist of several thicknesses 
in order to give it sufficient stiffness 
not to bend. Hold one end of each 
strip between the thumb and fore- 
finger. Move the hand till one strip 
is brought into position to coincide with one side of the 




REPRESENTATIVE OR PICTORIAL DRAWING. 71 

angle to be measured and then move the other strip till it is 
coincident with the other side of the angle. The strips of 
paper open like a pocket knife. (See Fig. 2.) 

In drawing objects begin with the simplest forms and with 
those that will present but small difficulties of perspective. 
Fasten a palmleaf fan upon the wall in front of you and 
study its outline and radiation of veining, and draw. Change 
its position to an oblique one and try again. Draw it in 
every way in which you will get its outline in nearly its true 
shape. Notice any little defects in the fan, a broken edge, 
a loose thread, etc. , and try to represent them. 

Avoid hard, smooth outlines and endeavor to make your 
work look artistic. - 

An artist's palette, a handglass, a watchcase, all make ex- 
cellent subjects for the beginner to study. 

The sphere is the simplest 
object that can be studied as its 
outline remains always the same 
in whatever position it may be 
.placed. (Fig. 3.) 

Find the highest point on the 
sphere and notice that when the 
sphere is below the eye we see beyond the highest point. In 
drawing the simple outline of the sphere place a mark to in- 
dicate the highest point on its surface. 

It is better to draw the outline of the sphere without any 
guide-lines whatever and when it appears to you to be cor- 
rectly drawn, test with the pencil and rectify all inaccuracies. 
If drawn without the use of diameters the danger of flat- 
tening the quarters is much lessened, the student is not ham- 




73 INDUSTRIAL DRAWING. 

pered by the fear of being unable to hit the points, and the 
sphere may be studied as a whole rather than in parts. 

After the sphere has been studied carefully the straight 
line solids may be considered. 

To study convergence, stand in front of a row of desks at a 
little distance from them and with a long stick held at arm's 
length between the eye and the desk, measure the apparent 
length of the front desk from left to right, and compare with 
the length of the rear desk. Measure the aisles in the same 
way. Measure the front edge of the desk nearest you and 
compare with the back edge of the same desk. Do the same 
to other desks at different distances from you. Place a book 
upon the table and notice convergence in the same way. 
Next observe a sheet of paper laid upon the table. 

Be careful at this point that the object to be measured is 
directly in front of and below the eye. 

In taking all proportional measurements it is well to close 
one eye. 

Note the convergence of railroad tracks, of lines of tele- 
graph or telephone poles, of the streets on which you walk. 
Keep your eyes and mind open for convergence in all that 
you see, until you have accustomed yourself to make a men- 
tal note of it, almost unconsciously to yourself. 

Place a cube on the desk directly in front of and below 
the eye, and note the number of sides seen. Draw the front 
as seen, which will be a square, then take accurate measure- 
ments of the apparent width of the top from front to rear 
and compare with the height ol the front. Measure the back 
edge of the top and compare with the front edge and it will 
be found to appear much shorter, and the two side lines will 



REPRESENTATIVE OR PICTORTAL DRAWING. 



n 




converge till they are cut by this shorter line. As the cube 
has been placed directly in front of the observer the two re- 
treating lines must recede at equal rate, and the two angles 
formed by the meeting of the sides with the rear line will be 
equal, and the two lines, if 
continued, will'meet in a 
point directly above the cen- 
ter of the drawing. The 
point at which these lines 
meet is called the Point of 
Sight and the horizontal 
line drawn through the 
Point of Sight'is called the 
Horizon Line. 

The Horizon Line is assumed to be on the level of the eye 
and to be the line which bounds the sight in the distance. 
The space in which the object is represented is called the Pic- 
ture Plane and lis supposed to include only so much as the 
observer can see without altering the position of the head, — 
an angle of about sixty degrees. 

The extremities of the horizon line are called Distance 
Points as they are assumed to mark the limit of the sight to 
right and left. The point of sight will, of course, be a 
point between these two points. 

Place the cube in the same relative position to you as be- 
fore^but so that the back edge of the table on which it rests 
appears to be about one-third of the height of the cube above 
thel lower "edge. Draw this line and call it the table-line. 
(See Fig. "4.) 

r When teaching this point to your class see that the pupils 



74 



INDUSTRIAL DRAWING. 



understand clearly the meaning of this line, A little girl, 
one day, on being questioned as to its meaning, said it was 
"a handle." 

Take great care that the table line shall be level. 

When the cube has been carefully studied in this way- 
place a box in the same position and draw, noting all the 
differences between the box and the cube. (Fig. 5.) 

Next study the drawing of a book, first placed on end, and 
then lying on its side. (Figs. 6 and 7.) 




k=^ 



Study the cube placed a little to the left, and the center 
of the front on a level wnth the eye. It will be noticed that 
the upper half of the cube is above the horizon line and that 
the lower half is below the line, but that the retreating edges 
still meet in the point of sight, and therefore the upper re- 



REPRESENTATIVE OR PICTORIAL DRAWING. 



75 



treating edge slants downward, while the lower edge runs 
upward to the same point. (Fig. 8.) 




^r 



^^/ 



Draw a cube as if placed with its center on the level of 
the eye and to the right of the observer (Fig. 9.) 

Represent a hollow box in the same position having the 
opening on the front (Fig. 10.) 










/ 






9s/ 










M^.. 4^. 


y^« 




/ 


^ 







76 Industrial drawing 

Draw a cube with its iipper edge on the horizon line and 
placed to the left of the point of sight (Fig. ii.) 

Draw a cube with its lower edge on the level of the eye 
and to the right of the point of sight (Fig. 12.) 

Draw a cube above the point of sight and in front of the 
eye. 

Observe that if the cube is placed on the horizon line and 
directly in front of the eye but one face, the front, can be 
seen which will appear in its true shape, a square, and if 
placed to the right or the left, whether on, above, or below 
the horizon line, if parallel to the observer, will still appear 
in its true shape. 

It is true that distance to the right or left of the observer 
will cause an apparent convergence of lines, but as the pic- 
ture plane assumes to comprehend what can be seen by one 
position of the eye all objects within the picture plane will 
be represented in their true shape if parallel to the observer. 
Otherwise the drawing would appear distorted. 

Study again the retreating edges of the row of desks, the 
aisles, the top of the table, etc., but by placing yourself a 
little to the right of the objects. 

It will now be seen that instead of two sides, we see three, 
the top, the front, and the left side. 

While the point of sight must remain directly in front of 
the observer, the object is no longer between the eye and the 
point of sight but it is at one side of both, yet the lines re- 
ceding from us still appear to converge in that point. 

The object must be very carefully studied and all propor- 
tional measurements accurately taken to ascertain the exact 



REPRESENTATIVE OR PICTORIAL DRAWING. 



77 



amount of convergence, and it is done in this case by means 
of the pencil exactly as it was done in the first drawing of 
the cube. When all proportions are carefully noted the cube 
is to be drawn. 



It is not always necessary to draw the horizon line or to 
indicate the point of sight but they should be constantly 
kept in mind and sometimes in drawing more difficult objects 
they may be used to test the accuracy of the drawing. 



Fig. 13 represents the cube as 
placed below the eye and to the left 
of the observe. 




The drawing of the cube in this 
position may be followed by the 
drawing of boxes, groups of books, 
etc., placed in the same position. 



Do not foreet the table line. 




Simple combinations of the sphere and cube may now be 
studied. Draw the sphere a little to the left of the cube 
and both to the left of the observer (Fig. 14.) 



78 



INDUSTRIAL DRAWING. 




Notice that the ap- 
parent distance be- 
tween the two objects 
varies with the position 
of the observer. 

In representing the 
sphere in front of the 
cube, the circle must 
be drawn far enough 
away to allow for the 
thickness of the sphere 
(Fig- 1 5-) 

Remember that ob- 
jects near the observer 
are nearer the lower 
edge of the paper than 
those that are farther 
away. 

When the sphere is 
represented as stand- 
ing- upon the cube, it 
must be remembered 
that the sphere would 
not stand firmly on one 
edge of the cube but 

would be most at rest if placed in the center of the top. 

(Fig. i6.) 

In a perspective drawing the center of a face can easily be 
found by drawing the diagonals of the face, the center being 
the point at which the lines intersect. 




REPRESENTATIVE OR PICTORIAL DRAWING. 79 



To represent the sphere be- 
hind the cube, we must re- 
member that the sphere being 
of the same size of the cube 
will be confined within the 
extended lines of the cube, 




and while actually of the same size of the cube will appear 
t o be smaller, because farther away from the eye. (Fig. 17.) 

To "study the drawing of the cylinder in perspective take 
a sheet of paper half as long as it is wide, say 6" by 12", 
roll up as a cylinder and pin together carefully so that it can 
be freely handled. 

Hold the cylinder in front of and below the eye so you can 
see into it, raise it slowly watching the top, and notice that 
the higher it rises, or the nearer the level of the eye, the 
narrower the ellipse appears, until the eye level is reached 
when nothing can be seen but a straight line. 

Repeat this several times, raising and lowering it, until 
you have become familiar with the changes which appear to 
take place. Notice that the farther below the level of the 
eye the wider the ellipse appears, therefore the lower ellipse 
will be wider than the one at the top, and be careful to re- 
member this fact when drawing the cylinder. However, the 
variations for an ordinary cylinder will be slight. 

Great care must be taken in drawing the ellipses that they 
may be perfectly balanced about their axes. 

It is well to draw a center line on which to indicate the 
width, and to assist in getting a correct form. Draw the com- 



INDUSTRIAL DRAWING. 



plete ellipse at the bottom and 
when the correct form has 
been obtained the back half 
may be erased. The table- 
line must come somewhere 
above the farthest edge of the 
lower ellipse. (Fig. i8.) 

Using the paper cylinder 
again place the top on a level 
with the eye so that the edge 
will appear to be a straight 
line; now raise it very' slowly 
and observe that above the eye 
the front edge appears to curve 
upward. 

When the middle of the cyl- 
inder is on a level of the eye, 
notice that the top seems to 
curve upward and the bottom 
to curve downward. (Fig. 19.) 



When drawing the table line it is necessary to put it back 
far enough to escape the back edge of the cylinder. 

Hold the cylinder on the level of your eye again, close one 
eye so as to look from one point and you will observe that 



REPRESENTATIVE OR PICTORIAL DRAWING. 



81 



yov cannot see qnite half around the cylinder. (Fig. 20.) 



J^.2C 



Mark the farthest distance you can see on each side without 
moving the head and then compare with the diameter of the 
circle. It will then easily be seen that the long diameter, or 
major axis, of the ellipse will not coincide with the diame- 
ter of the circle. 



'^- 



AB in Fig. 21 represents the di- 
^ ameter of the circle and CD the 
^ major axis of the ellipse. 

Next study the hollow cylinder, 
and for this it will be best to use a 
wooden one whose sides are about 
one-half inch thick. Observe its 
peculiarities, and notice first that 
the long diameter of the inner 
ellipse is not coincident with the 
major axis of the outer ellipse, and 
neither of them coincide with the 
diameter of the circle, but that the 
major axis of the inner ellipse is 
nearer the diameter of the circle than is the outer one. 




INDUSTRIAL DRAWING. 



If an indefinite series of ellipses were drawn, the smallest 
would be found to coincide with the center of the circle. 

By studying our cylinder again we find that the rear edges 
of the two ellipses appear to be nearer together than the front 
edges, also, that while the true thickness of the cylinder is 
seen at the ends of the major axis, there is a visible fore- 
shortening directly in front. (Fig. 22.) 

It would be well at this point to draw a square and inscribe 
a circle which touches all of the sides of the square. Have 
the drawing on cardboard or stiff paper so it can be held per- 
fectly level without bending. 

Study the appeai'ance of this figure exactly as you studied 
the top of the cylinder, and note carefully all apparent vari- 
ations in the circle, from the straight line, through all the 
widening ellipses till a full circle is reached. Observe care- 
fully the apparent place of the diameter of the ellipse in the 
different positions. 

Next inscribe another circle whose diameter shall be two- 
thirds of the larger circle. The circles must be concentric. 

Now study again, and find apparent difference of position 
of the major axes of the two ellipses. 

Fig. 23 shows the manner 
of drawing the figure to be 
studied. 

Fig. 24 shows the card as 
it will appear when held be- 
low and in front of the eye, 
and by studying it we ob- 
serve that I — 2 passes 
through the center of the 




REPRESENTATTVE OR PTOTORrAL DRAWING 




square, which is found by 
the intersection of the diag- 
onals, and is therefore the 
center of the circle, but the 
major axes of the ellipse is 
some distance in front of 
this and is indicated by 
3—4- 

This is explained by the principle that when the figure is 
on a plane parallel to the eye one line being nearer to the 
observer may appear longer than the diameter of the circle. 

After careful study of the cylinder it will 
be readily seen that the cone presents al- 
most no difficulties worthy of the name, 
however, there are two points to which 
we wish to direct your attention. 

Hold the cone in front of and below the 
^"^ eye and you will observe that you can see 
more than half-way around. (Fig. 25.) 

Invert the cone however and it will be 
observed that you can see less than half- 
way around. (Fig. 26.) 

If the cone is held in its true position 
but above the eye, less than half-way round 
can be seen. 

To represent the half-sphere draw first the outline of the 
whole sphere, then bisect the circle and represent the plane 




84 



INDUSTRIAL DEAWING. 



face as a circle seen in perspective, that is, an ellipse. Figs. 
27 and 28 will show what is meant without further explana- 
tion. 





Simple modifications of the type solids will readily suggest 
themselves and the student will do well to attempt the draw- 
ing of such as occur to him, applying, however, the same 
principles as have been here given. 





Remember that ivhere an edge is there must be a line^ or, 
in a perspective drawing there must be an ellipse if the ob- 
ject is curved. Lines also represent outlines or the parts that 
appear to be farthest out on the object. (Fig- 29.) 

We have already studied 'the cube in parallel perspective, 
/. e. , with one face or side parallel to the observer, and we 
must now consider it from another point of view, namely: 
with an angle turned towards us. 



REPRESElNfTATIVE OR PICTORIAL DRAWmG. 



85 




the edges appear to retreat to the point of sight, but that the 



This comes under 
the head of angular 
perspective and gives 
us several new points 
to consider. 

Place a cube in front 
of you and study it. 
Turn it so that one ver- 
tical edge will be di- 
rectly in front of you, 
that is, between you 
and thepoint of sight, 
and you will at once 
perceive that none of 



edges on the right go to some point in that direction, and 
those on the left to some point at your left, and that both 
points must be situated on the same level, or on the same 
Horizon Line. 

It will also readily be seen that if the object is placed di- 
rectly before the observer, and it is turned at an angle of 45 
degrees, that both the edges on the right and those on the 
left if extended would meet at equal distances from the Sight 
Point. 

These points at the right and the left are called "Distance 
ID? . ?s m' 



86 INDUSTRIAL DRAWING. 

Points," and in drawing, care shonld be taken that they are 
not placed too close to the point of sight, nnless the result is 
to be very small, as it would make the drawing appear dis- 
torted. At this point in your work it is well to be re- 
minded of an important principle: ' All vertical lines remain 
vertical. 

To draw an object in angular perspective, locate first the 
nearest vertical line then find or draw the line on the level of 
the eye. Find apparent slopes of the right and the left upper 
edges and extend these lines to the distance, or vanishing 
points. ' t)raw the lower lines to the same vanishing points. 
Use the pencil at this point to determine the apparent width 
of the right and left faces and draw their back edges, being 
very careful that these lines are vertical. 

To draw the top of the cube you have only to connect the 
upper end of the right vertical with the left distance point, 
and the upper end of the left vertical with the right distance 
point. If your work is correct in drawing the cube at an 
angle of 45 degrees the rear angle of the top will be directly 
above the front veVtical. 

_ Study the cube place at an angle of 45 degrees, but moved 
a little to the left of the observer, and it will be seen that the 
lines appear to retreat to the same distance points as before, 
but much more can be seen of one side of the cube than of 
the other. This dilference of apparent width can easily be 
determined by the use of the pencil for measurements,' (See 
Fig. 31.) 



REPRESENTATIVE OR IMCTORIAL DRAWING 



87 



ID.? 





Place the cube to the right of the Point Sight and farther 
from the observer and note difference in appearance. (Fig. 
32.) 



Draw the cube to the left 
and a little belov^ the eye 
and placed at right angle of 
45°. Change to an open 
box. (Fig. 33.) 



Draw a cube placed directly in front 
of, and below the eye, but turned at 
an angle of 60° to the right. Note 
that the distance point at the left 
seems much nearer the Point of Sight, 
and the one to the right seems much 
farther away. (Fig. 34.) 

Place a cube directly in front of you and so that the level 
of the eye shall be in th& center of the cube, then turn it to 
an angle of 45". Study convergence of lines and notice 
that the horizontal lines above the eye retreat downward to 
the distance points, while those below the eye appear to run 
upward to the same points. (Fig. 35.) 




88 



INDUSTRIAL DRAWING. 




The square prism and the square plinth may be studied 
under exactly the same conditions as the cube, and a few ex- 
amples of each will be sufficient to give a clear idea of their 
drawing. 

In drawing from the model it will be well to remember 
that the square prism is usually twice as tall as it is wide, and 
that the square plinth is three times as wide as high. 

Draw the square prism standing one square end to the left 
and below the eye. (Fig. 36.) 

Draw the square prism under the same conditions except 
that the prism shall be placed on one oblong side. (Fig. 37.) 




REPRESENTATIVE OR PICTORIAL DRAWING. 



The drawing of the square 
pyramid does not present any 
special difficulties. Draw it first 
as it appears to you, and after- 
ward test your work by drawing 
the diagonals of the base. If 
the pyramid is drawn correctly 
the apex will be situated directly 
over the center of the base. 
(Fig. 38-) 



The triangular prism should now be studied, but all points 
may be gained in the drawing of this model as in previous 
ones, by careful and continual use of the pencil for meas- 
urements. 




Draw the right-angled triangular prism standing on one 
triangular base, the right-angle being directly in front of 
and below the eye. 

The drawing must proceed in ex- 
actly the same way as for the square 
prism until the front faces are located 
and drawn. (Fig. 39.) 

If, however, the prism is to be drawn 
lying on one side and turned at an 
angle, we have a new point to consid- 
er. In parallel perspective we have 
but one set of retreating lines, therefore but one vanishing 
point; in angular perspective we found two sets of retreating 
lines and two vanishing points; now we find three sets of re- 
treating lines and so we must have three vanishing points. 




90 



INDUSTRIAL DRAWING. 




It Will be seen in 
Figs. 40 and 41 that 
the lines retreating up- 
ward appear to con- 
verge and would meet 
directly above vanish- 
ing point I, or on the 
horizon of the vertical 
plane. 




Tip a cube so that the 
rear is lifted a little and no- 
tice the pairs of parallel 
lines and their apparent van- 
ishing points, and while we 
have but two vanishing 

points this is also in obliqu^, perspective be- 
cause none of the lines are horizontal to the 
picture plane, and both sets of retreating 
lines vanish in a vertical horizon line rather 
than in a horizontal one. (Fig. 42;) 



KEPKEiriENTATlVE OR PICTORIAL DRAWING. 



If a face of the object is parallel with the horizon line it 
is in parallel perspective. If it is placed at an angle and an 
edge is nearest the observer it is in angular perspeciive. If 
an angle is nearest the eye and all the edges obliqne, it is in 
oblique perspective. 



/5^ 




n n p 



In grouping remember that two objects cannot occupy the 
same space, therefore two ellipses must not entercept one 
another. (Fig. 44-) 




92 INDUSTRIAL DRAWING. 

A group should consist of at least three objects, one of which 
should be larger than the others, or placed in a more promi- 
nent position. The objects should never be placed in a 
straight line. It is well, often, to place the objects in a tri- 
angular form, and to have part of them partially concealed 
behind the others. If any one of the group is inclined, it 
should have something to rest upon, thus indicating repose. 
As a rule the objects should not be placed at right angles to 
one another, nor to the edge of the paper. 

A few principles of perspective are here given for the stu- 
dent's consideration: 

1. Horizontal distance shorten lines. 

2. Vertical lines always remain vertical and grow shorter 
as they recede from the eye. 

3. Lines and surfaces presenting a front view appear of 
their actual form and in their true position. 

4. Surfaces seen obliquely are foreshortened in direct pro- 
portion to the amount of obliquity. Foreshortening is the 
apparent lessening in width when a surface is seen obliquely. 

5. Receding horizontal lines, if above the eye, appear to 
incline downward as they recede; if below the eye, they ap- 
pear to run upward; if on a level with the eye, they appear 
horizontal. 

6. Parallel horizontal lines vanish to the same distance 
points. 

7. Horizontal lines parallel to the line of vision converge 
to the point of sight. 

8. A circle seen in perspective is always an ellipse, or if 
on the level of the eye, a straight line. 

9. Equal circles when seen in perspective will vary in 
width according to relative distance below the eye. The 
farther below the level of the eye, the wider the ellipse. 



EEPRESENTATTVE OR PICTORIAL DRAWING- 




PAPER FOLDING, CLAY MOLDING, 

AND 

STICK LAYING. 



PAPER FOLDING. 



Paper folding is of value in teaching neatness, precision, 
attention, and strict obedience to command, in developing 
the power and dexterity of the hand, and in training the 
eye to see accurately and the mind to judge correctly. 

Paper folding is done with squares, triangles, oblongs and 
circles. The paper must be very accurately cut in order to 
insure good work. 

Squares four inches in size are ordinarily used, though for 
some forms it is well to use six inch squares. 

Have the paper laid upon the desk with one edge nearest 
you. Always fold from you and never take the paper from 
the desk in folding if it is possible to avoid doing so. 

From the square placed before the pupil, teach terms, 
edge, corner, upper edge, lower edge, upper right and left, 
lower right and left, applied to corners. 

Fold the lower edge of the paper to the upper edge. Turn 
the paper and hold it partly open and let the children read 
stories from their "books." 

A square of white paper may be folded in the same way 
and then pinned neatly inside of the colored square. The 
children may write a little story and their names in the 
book. lyct pupils draw a picture of the book on the board. 

Fold another square like the first, open it, and teach term 
diameter. Turn the jDaper so that the crease will point 



PAPER FOLDING. OLAV MOLDING, ETC. 97 

towards you and fold the lower edge to the upper edge. 
Open, and you have a window with four panes. Let pupils 
draw upon the board. 

Note. Dash lines indicate creases, but when the pupil 
draws upon the board he will make all his lines full lines. 

Fold a square as above, turn /'\ 

the paper cornerwise, and fold the / \ \^ 

corner nearest you to the upper cor- / I \, 

ner. Open. Teach diagonal^ and / | \^ 

review triangle. The children if <(- -|- y 

questioned, will tell you they 1 have \^ \ / 

made a shawl. Open the paper, \. j /; 

turn, and fold the other diagonal. \. i Z^'- 

Open and note triangles, and let pu- \i/ 

pils draw upon the board. We sometimes get this form of 
window in the upper end of a house or barn. (Fig. r. ) 

Using the same square, fold the corners to the center of 
the square. Open one corner and you will have the open 
envelope. 

The use of little gilt stars to fasten the three corners to- 
gether, letting the star project so the fourth corner may be 
folded under it, adds much to the child's delight, and may 
be used as a stimulus to neatness and accuracy by placing 
them only upon the neatest and most accurate folding made 
in the lesson. 

Let pupils draw the closed envelope on the board, let them 
draw the open one also, then allow them to write a little 
story, fold, and place within the envelope. 



98 



INDUSTRIAL DRAWING 




Fold the diameters and diagonals of a 
square, fold the corners to the center; the 
result being the same as the closed enve- 
lope. Without opening turn the folding 
over. Turn the small square cornerwise, 
and fold the corners to the center of the 
square. Care must be taken that the paper 
does n(?t slip or crush, but folds easily in the creases made in 
the folding of the diagonals. Fold the corners to the center 
of the sides. Result — a picture frame. (Fig. 2.) 

Let the children have these foldings to take home, and 
many of them will bring them back to show the little pic- 
tures they have framed in them. 

Many of the foldings as taught in the kindergarten are in 
series of six, each one of a series being one step in advance 
of the preceding one. A few of these series are given and 
many others can be made by the teacher by exercising a 
little thought and ingenuity. 

Take a square, fold the lower edge to the upper edge, open 

the paper, fold the lower edge to the middle crease, turn the 

paper so that the upper edge will be nearest you, fold this edge 

to the middle crease, and open the paper and 

there are disclosed four oblongs. Turn the 

paper so that the creases will bevertical, 

fold as before, and open, and sixteen small 

squares will be seen. All the series here 

given will start with the sixteen small 

?7-' squares. (Fig. 3.) 

Fold one diagonal, open, fold the other diagonal and open 
the paper. Turn the paper over. At this juncture much 
depends on turning the paper over. Turn the corners to the 






PAPER FOLDING. CLAY MOLDING, ETC. 



center of the square. Open the paper very carefully, turn it 
over and stand it on the four corners. (See Fig. 4.) Taking 
hold of one corner, tap lightly on A, and let the creases bend 
downward at this point. Repeat at each corner, and you 
will have the basket. (Fig. 5. ) 





Turn the middle of each side to the center, and fold the 
corners as squares. You will then have one square on the 
back of your folding and four small squares on the front. 
(Fig. 6). This is No. i of the first series. No. 2 is formed 
by turning the corners back to the corners of the large 
square. (Fig. 7.) The remainder of the series are shown in 
Figs. 8, 9, 10 and 11. 








100 



INDUSTRIAL DRAWING. 



The next series begins like the first and progresses in the 
same order nntil Fig 6 is reached. The six fignres are illns- 
trated in Figs. 12, 13, 14, 15, 16 and 17. 




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Series 3 begins as the first series did and continnes the 
same till Fig. 6 is reached. The small sqnares are now 
folded from their outer corners to the center of the sides. 
(Fig. 18.) The series continues in the 
same order as the preceding ones. 

Series 4 is folded in the same manner 
as the others nntil Fig. 6 is reached. The 
small squares are now folded obliquely from 
the center of the large square to the center 
of the side of the small square. Fig. 19 
will show the first of this series. The re- 
maining steps are like those already shown. 
Series 5 is folded like the others till Fig. 
6 is reached, and then it becomes a combi- 
nation of Series 3 and 4. The corner of 
the small square is folded from the outer 



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PAPER FOLDING, CLAY MOLDING, ETC. 



101 



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corner, and the opposite corner is folded 
from the center. (Fig. 20.) The succeed- 
ing steps are the same as heretofore. 

These series may be varied or added to 
in numberless ways. Fig. 21 shows one 
similar to Fig. 18, except that the corners 
are turned outside instead of being hid- 
den as in Series 3. 



Many variations may be made by fold- 
ing the small triangles in the center. 
Fig. 22 will illustrate this. 

To fold a boat with two sails, fold one di- 
ameter, open, fold the other diameter and 
open. Turn the paper over, and fold both 
diagonals taking care to open the paper 
each time. We find by taking up the pa- 
per that the diagonal creases bend outward 
and the diameters toward the inside of 
■^^ the paper. Hold the paper lightly in 

the hand with the corners turning upward. Puslf lightly on 
the spot where the creases intersect until it forms the top and 
the corners turn down. (Fig 23.) Draw the right and the left 
corners together, press down the two out- 
side squares and you have a small square 
showing. Turn the paper around and hold 
by the corner which coincides with the cen- 
ter of the large square. Take the upper 
corner of the square nearest you and fold 
to the lower corner. Do the same to the 
qsuare at the back. This will leave the two sails standing. 



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102 



INDUSTKIAL DRAWING. 



Lift Up the corners of the squares just folded down and fold 
back to the center creases. Nowtaketheheavy triangle remain- 
ing and fold it to the center crease. The three foldings at 
the bottom must be hidden and the creases firmly pressed 
down to make the bottom of the boat firm. Let the pupils 
sail their boats on their desks by blowing them gently along. 
Fig. 24 shows the completed folding. This folding forms a 
very good subject for a drawing lesson, and also for a lan- 
guage lesson. 

With another square fold the sixteen 
small squares and the diagonals, turn the 
paper over and fold corners to the cen- 
ter. Proceed until Fig. 5 is reached. 
Push centers of sides together and hold- 
ing lightly in both hands, fold on one 
diagonal of the small square at the back. 
Fold on the diagonal of each small 
square, letting one come to the right and 
the other to the left. For this folding 
the children have several names, saw 
horse, vase, etc. The children like to 
press flowers and fasten them m their 
vases. (Fig. 25.) 



To make a boat, fold as for Fig. 25. 
then turn the lower right corner back 
to the lower left corner. (Fig. 26.) 

For a woman in a sun-bonnet sitting 
in a boat, fold as for Fig. 26, then fold 

the upper triangle inside. (Fig. 27.) 





PAPER FOLDING, CLAY MOLDING. ETC. 



103 



The chicken (Fig. 28) is folded from 
Fig. 26, by opening partially and tnrn- 
ing the triangle at A wrong-side ont and 
letting the other parts remain as before. 



^r 



The dnck (Fig. 29) is made by fold- 
ing as in Fig. 28 and then opening the 
squares at A and folding back to the 
sides. 



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Some beautiful work may be done by 
using equilateral triangles, four inches 
on a side. The folding is so much like 
that for the square that it will be unnec- 
essary to explain except by a few illus- 
trations. (Figs. 30, 31, 32.) 




CLAY MODELING. 



Clay modeling is valuable as a means of form study. It 
cultivates observation and judgment, trains the eye, and 
develops the dexterity of the hand. 

Artists' clay is no doubt the best to use, but for all ordi- 
nary work common potters' clay serves every purpose. 

If clay is obtained at a pottery it is usually sent in a moist 
condition, and for a time requires no care except to keep it 
damp. Clay that is bought from school supply houses is sent 
dry and must be prepared by the teacher. If the clay has 
been purchased damp, wrap it in several thicknesses of wet 
cloth and place in a stone jar. When ready for use it should 
be of the consistency of stiff dough. If dry the clay must be 
pounded till reduced almost to a powder. Place it in a large 
cloth and tie it up. Put it in the jar and pour over water 
enough to cover the mass. Let it stay in the water several 
hours then take out the bundle and, without mitiyng, work 
the clay. This can be done in two ways: knead it as you 
would bread, or pick it up and drop it, turning it every time. 
A combination of the two ways is always good. When the 
clay has become smooth and plastic, it is ready for use. If 
the clay is too hard, moisten it again by pouring a little water 
over it and kneading it again. If it is too moist it must be 
allowed to dry off. 

Clay is like dough in that it is experience alone that can 
tell you when it is exactly of the proper consistency. When 
it is just dry enough not to stick badly to the hands, take it 



PAPER FOLDING, CLAY MOLDING, ETC. 105 

out ot the cloth and by lifting and dropping or by pounding 
it shape it into a brick. It is then ready to cut. 

Cut the clay with a strong, fine string or wire, the latter 
being preferable, into cubical pieces for the children. Inch 
cubes are large enough for the usual molding. 

A piece of oil cloth or paper should be spread upon each 
desk to protect the surface. A smooth board 12" by 18" 
will be found of great service to hold the clay when prepar- 
ing it for the class and also in collecting the clay. 

Children begin by molding the sphere, the first of the type 
solids. The block of clay is taken in the fingers and the 
shape produced by quick, light touches of the fingers and a 
continual turning of the mass — that is, by "finger manipu- 
lation." 

Sometimes the sphere is produced by rolling in the palms 
of the hands, but this is a more mechanical process, and does 
not cultivate the sense of touch as in the u^ of the fingers. 

It is necessary that the children have the small wooden 
models on their desks where they can compare their work 
with the perfect type. 

The next type solid is the cylinder, and this is best mod- 
elled by biiilding up. 

The child takes a small piece of the clay, with the fingers 
presses it into a small circular disc, and places it on his desk. 
The cylinder is built up on this base, not, however, by mak- 
ing a series of discs and placing upon one another but by ad- 
ding small irregular lumps and shaping to the general form 
after adding to the cylinder. In this method of working it 
is not necessary to take the work from the desk, but the cloth 
or paper on which it rests can be turned like a revolving 
table so the child can see all sides in turn. 



106 INDUSTRIAL DRAWING. 

The tendency will be for the child to make his model 
smaller at the top, but this can be corrected by calling his 
attention to that point. By light touches with the fingers 
and smoothing a little, all traces of joining can be obliterated. 

This method of working is preferable to obtaining the form 
by rolling, as there is not the likelihood of getting the hol- 
lows in the ends by too much rolling, or of making the ends 
project by too much patting of the ends to obtain the flat 
faces. 

The cube is the third and last of the type solids. 

When giving out the clay for this work it is better to give 
it in irregular masses than in the neatly cut cubical blocks. 
The reason for this is obvious. If the teacher it very skill- 
ful in cutting the clay, she has left the child too little to do, 
if she is not expert she has confused him by an apparent 
likeness. The c^be should be built as the cylinder was, and 
carefully worked with the fingers to obtain sharp, clean edges 
and corners. The method formerly used of tapping the .clay 
on the desk or of striking it with a flat stick, may, and does 
produce oftentimes a good form, but at the expense of many 
other valuable considerations. The noise also distracts at- 
tention from the result to be obtained and has been known 
to make the pupil more solicitous about the amount of phys- 
ical energy he is to use than of the true object of the lesson. 

The half-sphere is obtained by modeling the sphere and 
bisecting it. This is best done by the use of No. 60 thread. 
Take a piece about four inches in length, straighten upon 
the desk and lay the sphere carefully upon it. Draw the 
thread up by both ends, tie in a single knot and slowly and 
carefully draw the knot close to the clay. See that the 



PAPER FOLDING, CLAY MOLDING, ETC. 107 

thread lies evenly around the sphere and when accurately ad- 
justed pull steadily outward with both hands. 

The half-cube is obtained by cutting the cube on one diag-- 
onal. 

The half-cylinder by cutting the cylinder vertically. 

The square prism by cutting the cube on both diameters 
of the base. 

To obtain the circular plinth quadrisect the cylinder hoii- 
zontally. 

To obtain the square plinth mold a large prism and quad- 
risect horizontally. 

The right-angled triangular prism is obtained by cutting 
the square prism on one diagonal of the bases. 

MODIFICATIONS OF SOLIDS. 

Sphere — Apple, bead, cherry, baseball, grapes, vase, 
sugarbowl. 

Cylinder — Firecracker, mallet, rollingpin, bottle, pump, 
mug, water cooler. 

Cube — Bead, box, basket, bureau, ink bottle, house. 

Half-sphere — Half-apple, bowl, basket, cap, toadstool. 

Half-cylinder — Cradle, log of wood. 

Square prism — House, pump, cofifeemill. 

Triangular prism — Roof of house. 

Square plinth — Cracker, box, book. 

Circular plinth — Cakes, checkers, coins, cake basket. 

Flat spheroid — Turnip, beet, bonbon box, muskmelon. 

Long spheroid — Potato, lemon, melon. 

Cone — Oil can, funnel, churn, coffeepot, wineglass. 

Ovoid — Egg, pear, gourd. 



STICK LAYING. 



Stick laying- is of value in the teaching of form and arrange- 
ment. 

The first work in stick laying in form study comes after 
the type solids have been studied. 

Review terms: vertical, horizontal, oblique, square, trian- 
gle, oblong, diameter and diagonal, using sticks. 

Simple historic borders are also made, either by following 
the teacher who works at the blackboard or by dictation. 



Figs. I, 2, 3 and 4 will 
give some idea of work iu 
borders. Long sticks may 
be given for enclosing lines. 
Fig. 5 will give suggestions 
for advance work in borders. 



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PAPER FOLDING, CLAY MOLDING, ETC. 



109 



Below are given some arrangements, with 4, 5, 6, 7, 8 and 
9 sticks. This can be done from the blackboard or from dic- 
tation and the pupil mnst be encouraged to do original work. 




110 



INDUSTRIAL DRAWING 



The study of angles may be made interesting by using 
sticks, combining not more than three sticks to make angles 
up to twelve. It is impossible to make eleven angles with 
three sticks. Let the children dot the angles. 





Radial designs may also be made. 





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